Physics : Kinematics : Components of a Vector

**COMPONENTS OF A
VECTOR**

In
the Cartesian coordinate system any vector can be resolved into three components along *x, y* and *z* directions.
This is shown in Figure 2.20.

Consider
a 3-dimensional coordinate system. With respect to this a vector can be written
in component form as

**EXAMPLE 2.3**

**What are the unit vectors along the negative x–direction, negative y–direction, and negative z– direction?**

**Solution**

The unit vectors along the negative directions can be shown as in the following figure.

Then we have:

The unit vector along the negative x direction = -iˆ

The unit vector along the negative y direction = -jˆ.

The unit vector along the negative z direction = -kˆ.

In
the previous section we have learnt about addition and subtraction of two
vectors using geometric methods. But once we choose a coordinate system, the
addition and subtraction of vectors becomes much easier to perform.

The
two vectors and in a Cartesian coordinate system can
be expressed as

Then
the addition of two vectors is equivalent to adding their corresponding x, y
and z components.

Similarly
the subtraction of two vectors is equivalent to subtracting the corresponding
x, y and z components.

The
above rules form an analytical way of adding and subtracting two vectors.

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11th Physics : UNIT 2 : Kinematics : Components of a Vector | with Solved Example Problems

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